Wallace played the clip of the ad, which called Obama an "elitist hypocrite" for sending his children to a school with armed protection while opposing it for other schools. (That ad has actually been proven false.)

Wallace asked LaPierre if he regretted putting up the ad. He avoided the question and said the point of the ad was "not to pick on the President's kids."

Here's the most contentious exchange:

LAPIERRE: The President's kids are safe, and we're all thankful for that.

WALLACE: They also face a threat that most people do not face.

LAPIERRE: Tell that to the people in Newtown! Tell that to the people in Newtown.

WALLACE: Do you really think that the President's children are the same kind of target as every schoolchild in America? I think that's ridiculous, and you know it, sir.

Wallace pressed LaPierre on whether he believes every schoolchild is entitled to armed protection. He also challenged the NRA chief on the gaps in that theory: How they're not protected at the movie theater, the mall, and other places after they leave school.

The last contentious exchange came when Wallace disputed LaPierre's logic that only "elite, out of touch" politicians have armed protection next to them. Wallace pointed out that LaPierre also traveled with armed guards to his appearance on "Fox News Sunday."

"Does that make you an elite, and out-of-touch elite, because you have security?" Wallace said.

LaPierre said he didn't want to deny anyone the right to armed protection.